1. Routing Algorithms using Random Walks with Tabu Lists Karine Altisen & Stéphane Devismes Joint work with Antoine Gerbaud, Pascal Lafourcade, and Clément Ponsonnet ARESA 2

2. Disclaimer Today, we will speak about probabilities – But, we are not specialists … 22/02/11Meeting Synchrone2

3. Wireless Sensor Network (WSN) 22/02/11Meeting Synchrone3 Battery Sensor(s) Processor Radio

4. Routing 22/02/11Meeting Synchrone4

5. Application 22/02/11Meeting Synchrone5

6. Setting 22/02/11Meeting Synchrone6 4 4 8 8 3 3 9 9 5 5 6 6 1 1 7 7 2 2 One sink/Multi source Connected Identified Reliable Asynchronous Spontaneous requests

7. Random Walk 22/02/11Meeting Synchrone7 4 4 8 8 3 3 9 9 5 5 6 6 1 1 7 7 2 2 Rand(7,9,2) Rand(1,7,5,6,2) Rand(1,9,6) Rand(9,8,6,4,3)

8. Probability Laws Uniform (RW) – Let v,u two neighbors, v u – Problem: hitting time = O(N 3 ) 22/02/11Meeting Synchrone8

9. Probability Laws Biased (Yamashita et al) (RWLD) – Let v,u two neighbors, v u – standardize frequencies of visits, for all nodes – hitting time = O(N 2 ) 22/02/11Meeting Synchrone9

10. RW vs. RWLD 22/02/11Meeting Synchrone10

11. Routing by Random Walk Pros – Message length – Tight local computation and memory – No need of overlay – Load of the network –…–… Cons – Hitting time (average number of hops to reach the sink) O(N 3 ) (RW) and O(N 2 ) (RWLD) 22/02/11Meeting Synchrone11

12. Random Walk with Tabu Lists Add memory to help random walks – Avoid cycles Store hints about previous choices k where k is small – Good trade-off ? 22/02/11Meeting Synchrone12

13. Where ? Messages – Store IDs of visited nodes – Visit new nodes first Nodes – One list per destination – Store message ID – Detect cycles – cycle detections: visits 22/02/11Meeting Synchrone13

14. Full ? (Update policy) FIFO policy Rand policy 22/02/11Meeting Synchrone14

15. FIFO Policy Update(e,L) 22/02/11Meeting Synchrone15 abed abde abfdgz e

16. Rand Policy Update(e,L) 22/02/11Meeting Synchrone16 abde abfdgze Rand

17. Sum up Probability law: RW / RWLD Tabu Lists Location: node / message Tabu List size Update policies: FIFO / Rand 22/02/11Meeting Synchrone17

18. Tabu List in Messages (TLM) 22/02/11Meeting Synchrone18 4 4 8 8 3 3 9 9 5 5 6 6 1 1 7 7 2 2 Rand(7,9,2)=2 Rand(7,5,6)=5 Rand(9,6) = 9 Rand(8,6,4,3) = 3 [1] [1,2] [2,9] [9,5]

19. Tabu List & Counters in Nodes (TLCN)(1/2) 22/02/11Meeting Synchrone19 12 1 1 1 1 (12,1) 1 (23,8) (12,1) (23,8) 2 2

20. Tabu List & Counters in Nodes (TLCN)(2/2) Next destination ? 22/02/11Meeting Synchrone20

21. Experimentations (settings) Sinalgo (JAVA) Graphs: UDG, connected, one sink/multi-source, uniform distribution 100 messages per sources Data generation: [400..600] Transmission time: [40..50] List sizes: – TLM: 1 & 15 – TLCN: 15 Random Walk: RWLD Update: FIFO & Rand 22/02/11Meeting Synchrone21

22. Hitting time (1/2) 22/02/11Meeting Synchrone22

23. Hitting time (2/2) 22/02/11Meeting Synchrone23

24. Volume, e.g., sum |messages| 22/02/11Meeting Synchrone24

25. Convergence of TLCN 22/02/11Meeting Synchrone25

26. Sum up 22/02/11Meeting Synchrone26 Hitting TimeVolume Degree Sensitivity Load Sensitivity TLCN (15,FIFO)11noyes TLCN (15,Rand) 11noyes TLM (15,FIFO)37no TLM (15,Rand) 48no TLM (1,FIFO) 55no TLM (1,Rand) 66no RWLD73no RW84yesno

27. Analysis 22/02/11Meeting Synchrone27

28. NSC for TLM NSC: update rule finite average hitting time If the list is full and the current node is not in the list, then the probability of removing the oldest element is positive FIFO and Rand match the NSC 22/02/11Meeting Synchrone28

29. RW+TLM vs. RW (1/2) |List| 3, there exist graphs where RW is better than RW+TLM Ex. for 4 22/02/11Meeting Synchrone29 …

30. RW+TLM vs. RW (2/2) |List| = 1,2, RW+TLM is always better than RW 22/02/11Meeting Synchrone30 1 1 4 4 7 7 9 9 3 3 2 2 RW+TLM RW

31. RWLD+TLM vs. RWLD (1/2) For all size, there exist graphs where RWLD is better than RWLD+TLM – |List| 3, as previously – 2, to be done ! – 1: 22/02/11Meeting Synchrone31

32. RWLD+TLM vs. RWLD (2/2) Conjecture: In random graphs, RWLD+TLM is always better than RWLD 22/02/11Meeting Synchrone32

33. RW+TLM 1,2 vs. RWLD (2/2) There exist graphs where RWLD is better than RW+TLM 22/02/11Meeting Synchrone33

34. TLCN Is the hitting time finite ? In case +asynchronous, no 22/02/11Meeting Synchrone34 Sink Source 1

35. Thank you 22/02/11Meeting Synchrone35